scholarly journals Memory Effect in the Spatial Series Based on Diamond and Graphite Crystals

Molecules ◽  
2020 ◽  
Vol 25 (22) ◽  
pp. 5387
Author(s):  
Ludmila Grigoreva ◽  
Alexander Razdolsky ◽  
Vladimir Kazachenko ◽  
Nadezhda Strakhova ◽  
Veniamin Grigorev
Keyword(s):  
Long Memory ◽  
Interatomic Distance ◽  
Materials Science ◽  
Calculated Data ◽  
Fluctuation Analysis ◽  
Spatial Series ◽  
Power Spectral ◽  
Fractal Properties ◽  
Allotropic Modifications ◽  
Detrended Fluctuation

To study the relation between the structure of a compound and its properties is one of the fundamental trends in chemistry and materials science. A classic example is the well-known influence of the structures of diamond and graphite on their physicochemical properties, in particular, hardness. However, some other properties of these allotropic modifications of carbon, e.g., fractal properties, are poorly understood. In this work, the spatial series (interatomic distance histograms) calculated using the crystal structures of diamond and graphite are investigated. Hurst exponents H are estimated using detrended fluctuation analysis and power spectral density. The values of H are found to be 0.27–0.32 and 0.37–0.42 for diamond and graphite, respectively. The calculated data suggest that the spatial series have long memory with a negative correlation between the terms of the series; that is, they are antipersistent.

scholarly journals A Survey on Efficiency and Profitable Trading Opportunities in Cryptocurrency Markets

2019 ◽  
Vol 12 (2) ◽  
pp. 67 ◽  
Author(s):  
Kyriazis
Keyword(s):  
Long Memory ◽  
Detrended Fluctuation Analysis ◽  
Efficient Market Hypothesis ◽  
Trading Strategies ◽  
Fluctuation Analysis ◽  
Efficient Market ◽  
Systematic Survey ◽  
Rescaled Range ◽  
Pricing Behavior ◽  
Detrended Fluctuation

This study conducts a systematic survey on whether the pricing behavior of cryptocurrencies is predictable. Thus, the Efficient Market Hypothesis is rejected and speculation is feasible via trading. We center interest on the Rescaled Range (R/S) and Detrended Fluctuation Analysis (DFA) as well as other relevant methodologies of testing long memory in returns and volatility. It is found that the majority of academic papers provides evidence for inefficiency of Bitcoin and other digital currencies of primary importance. Nevertheless, large steps towards efficiency in cryptocurrencies have been traced during the last years. This can lead to less profitable trading strategies for speculators.

FRACTAL PROPERTIES OF PARTICLES IN PHASE SPACE FROM URQMD MODEL

2013 ◽  
Vol 22 (04) ◽  
pp. 1350021 ◽  
Author(s):  
X. WANG ◽  
C. B. YANG
Keyword(s):  
Phase Space ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Two Dimensional ◽  
Urqmd Model ◽  
Fractal Properties ◽  
Dynamical Fluctuations ◽  
Detrended Fluctuation

Nonstatistical dynamical fluctuations by means of the detrended fluctuation analysis (DFA) and multifractal DFA are studied. We used a two-dimensional algorithm for the analyses. By choosing different particles generated by UrQMD code, we show that different particles all have good scaling behaviors with bin size. The correlation between different identified particles are also discussed.

scholarly journals Trends, noise and re-entrant long-term persistence in Arctic sea ice

2012 ◽  
Vol 468 (2144) ◽  
pp. 2416-2432 ◽  
Author(s):  
S. Agarwal ◽  
W. Moon ◽  
J. S. Wettlaufer
Keyword(s):  
Sea Ice ◽  
Time Scales ◽  
Seasonal Cycle ◽  
Arctic Sea Ice ◽  
Fluctuation Analysis ◽  
Fractal Properties ◽  
Arctic Sea ◽  
Original Record ◽  
Detrended Fluctuation

We examine the long-term correlations and multi-fractal properties of daily satellite retrievals of Arctic sea ice albedo and extent, for periods of approximately 23 years and 32 years, respectively. The approach harnesses a recent development called multi-fractal temporally weighted detrended fluctuation analysis, which exploits the intuition that points closer in time are more likely to be related than distant points. In both datasets, we extract multiple crossover times, as characterized by generalized Hurst exponents, ranging from synoptic to decadal. The method goes beyond treatments that assume a single decay scale process, such as a first-order autoregression, which cannot be justifiably fitted to these observations. Importantly, the strength of the seasonal cycle ‘masks’ long-term correlations on time scales beyond seasonal. When removing the seasonal cycle from the original record, the ice extent data exhibit white noise behaviour from seasonal to bi-seasonal time scales, whereas the clear fingerprints of the short (weather) and long (approx. 7 and 9 year) time scales remain, the latter associated with the recent decay in the ice cover. Therefore, long-term persistence is re-entrant beyond the seasonal scale and it is not possible to distinguish whether a given ice extent minimum/maximum will be followed by a minimum/maximum that is larger or smaller in magnitude.

scholarly journals Source Of The Multifractality In Exchange Markets: Multifractal Detrended Fluctuations Analysis

2014 ◽  
Vol 12 (4) ◽  
pp. 371
Author(s):  
Samet Gunay
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Long Memory ◽  
Detrended Fluctuation Analysis ◽  
Autoregressive Process ◽  
Fluctuation Analysis ◽  
Fat Tails ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Exchange Markets ◽  
Detrended Fluctuation

In this study, we analyzed the multifractality and the source of multifractality of the returns of GBP/USD, EUR/USD, USD/JPY and USD/CHF currencies. In the examination of multifractality we performed the Multifractal Detrended Fluctuation Analysis (MF-DFA). Also, we used shuffled and surrogated data that was derived from the Statically Transformed Autoregressive Process (STAP) method to determine the source of multifractality. According to the results, GBP/USD returns have monofractal features, whereas EUR/USD, USD/JPY and USD/CHF returns have multifractal behaviours. The tests concerning the source of multifractality indicated that the reason of multifractality for EUR/USD and USD/JPY returns is fat-tails of the probability density function of returns, whereas the reason of multifractality of USD/CHF returns are both long memory and fat tails. Also we have seen that there is an ambiguous relationship between the liquidity of the currency market and multifractality.

scholarly journals Nonlinearity and Fractal Properties of Climate Change during the Past 500 Years in Northwestern China

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Shiquan Wan ◽  
Qunqun Liu ◽  
Jianxin Zou ◽  
Wenping He
Keyword(s):  
Climate Change ◽  
Nonlinear Process ◽  
Northwestern China ◽  
Fluctuation Analysis ◽  
The Past ◽  
Fractal Properties ◽  
Change Characteristics ◽  
Range Correlation ◽  
Detrended Fluctuation

By using detrended fluctuation analysis (DFA), the present paper analyzed the nonlinearity and fractal properties of tree-ring records from two types of trees in northwestern China, and then we disclosed climate change characteristics during the past 500 years in this area. The results indicate that climate change in northwestern China displayed a long-range correlation (LRC), which can exist over time span of 100 years or longer. This conclusion provides a theoretical basis for long-term climate predictions. Combining the DFA results obtained from daily temperatures records at the Xi’an meteorological observation station, which is near the southern peak of the Huashan Mountains, self-similarities widely existed in climate change on monthly, seasonal, annual, and decadal timescales during the past 500 years in northwestern China, and this change was a typical nonlinear process.

ABOUT THE EFFECTIVENESS OF DIFFERENT METHODS FOR THE ESTIMATION OF THE MULTIFRACTAL SPECTRUM OF NATURAL SERIES

2010 ◽  
Vol 20 (02) ◽  
pp. 331-339 ◽  
Author(s):  
ALEJANDRA FIGLIOLA ◽  
EDUARDO SERRANO ◽  
GUSTAVO PACCOSI ◽  
MARIEL ROSENBLATT
Keyword(s):  
Wavelet Analysis ◽  
Multifractal Spectrum ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Natural Systems ◽  
Fractal Properties ◽  
Wavelet Leaders ◽  
Self Similar ◽  
Detrended Fluctuation ◽  
Natural Series

Complex natural systems present characteristics of scalar invariance. This behavior has been experimentally verified and a large related bibliography has been reported. Multifractal Formalism is a way to evaluate this kind of behavior. In the past years, different numerical methods to estimate the multifractal spectrum have been proposed. These methods could be classified into those that originated from the wavelet analysis and others from numerical approximations like the Multifractal Detrended Fluctuation Analysis (MFDFA), proposed by Kantelhardt and Stanley. Recently, S. Jaffard and co-workers proposed the Wavelet Leaders (WL) method that exploits the potential of wavelet analysis and the efficiency of the Multiresolution Wavelet Schema. In a previous work, we checked that both methods are equivalent for estimating fractal properties in a series from singular measures. Now, we apply MFDFA and WL to natural signals with self-similar structures, but unknown multifractal spectrum. We observe that some differences appear in their respective estimations, particularly when the signals are corrupted with fractional Gaussian noise.

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